cs-012 — Guess and Check
| Field | Value |
|---|---|
| id | cs-012 |
| difficulty | Advanced |
| topics | flowchart, game loop |
| lecture | lecture-03 |
| estimated time | 5-minute attempt + 10-minute discussion |
| prerequisites | functions, dictionaries, and earlier algorithmic patterns |
| objective | design the algorithm, verify it on edges, and argue correctness or trade-offs |
| solution | held by the instructor; discussed after the attempt |
Problem
A number-guessing game with 'higher/lower' feedback. Flowchart the loop and argue how many attempts it can take before the loop must end.
Your deliverable is the stated assumptions, the rule list, the decision for the worked instance, and one contested case. If the problem is ambiguous anywhere, state the assumption you are making and carry on — a stated assumption is part of a good answer.
Examples
- Input: secret 73, range 1..100; guesses 50 (low), 87 (high), 68 (low), 74 (high)
- Output: 6 guesses or fewer always suffice for 1..100 (ceil(log2 101) = 7, achieved 6 here)
Solve for the worked instance first. Then ask what would change if one number, name, or condition were replaced by something stranger.
What to notice
- Halving argument: each answer discards half the remaining range; count the halvings.
- Writing the rules IS the solution; code is transcription.
- Every assumption is a place where two good answers can differ.
Discussion starter
After the solution is revealed, the class spends five minutes on this prompt: "Which assumption would you attack first if you had to argue the other side?"
Constraints and assumptions
- Difficulty: Advanced (functions, dictionaries, and algorithmic reasoning assumed).
- Topics: flowchart, game loop.
- Classroom-scale inputs unless the problem says otherwise.
- Time-box: about five minutes for a defensible plan; a complete solution may take longer and that is expected - state where you would resume.
- Optional stretch (not required): describe an alternative approach and say when it beats the obvious one.
Hints and extension
- First nudge: identify the pattern the worked instance uses before computing anything.
- If stuck after three minutes, write the input/output line you expect and trace the smallest example by hand.
- After the reveal, attempt the extension below before the next lecture.
- Extension challenge: Redraw the flow with one extra decision diamond and argue what changes.